The Expectations Hypothesis
Kerry Back

Forward Curve
The forward curve shows the prices of contracts for different delivery dates.
It shifts up and down over time as prices change.
Its slope can also change.
The front month price is the “spot price” - i.e., the price for (near) immediate delivery.
Gold Forward Curve
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Gold forward curve on 1-24-2022.
Expectations hypothesis
- The expectations hypothesis is: The futures price is equal to the market’s expectation of what the spot price will become.
- Example: maybe the market expected on 1-24-2022 that gold would hit $2,000 in 8 years.
- The expectations hypothesis is reasonable, though there is risk and there may be risk premia.
Expectations and the forward curve
- Expectations affect not just the futures price but also today’s spot price.
- Example: If we think gold will hit $2,000 in 8 years and it is trading at $500 today, then we should all be buying gold today (quadruple our money in 8 years).
- This drives up the spot price to the point that we would only get a “normal” return on spot gold.
- Ignoring risk and risk premia, if we think gold will hit $2,000 in 8 years, then today’s spot price should be \(\text{2,000} / (1+r)^8\).
- So, futures in 8 years (2,000)should equal spot \(\times (1+r)^8\)
- In fact, the forward curve should be rising by the factor \(1+r\) each year.
Contango
A market is in contango if the forward curve is upward sloping, as in the gold example.
In other words, you pay more for future delivery than in the spot market.
The term originates from deferring purchase of a stock. You had to pay a fee to postpone settlement.
Contango is natural, because of the time value of money. But, there are other factors.
Backwardation
- A market is in backwardation in the opposite situation: the forward curve is downward sloping.
Stock Index Futures in Backwardation
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S&P 500 forward curve on 1-24-2022
Backwardation and Expectations Hypothesis
- According to the expectations hypothesis, the market expected stock prices to fall on 1-24-2022.
- Did people expect to lose money on stocks?
- No. Part of the stock return is the dividend. According to the expectations hypothesis, the market expected to earn the risk-free rate on stocks as dividends + capital gain.
- Dividends > interest \(\Rightarrow\) capital gain < 0.
Summary
- Expectations hypothesis is “futures price = expected future spot price.”
- Expectations affect both the futures price and the spot price.
- Markets can be in contango (rising futures price and futures > spot) or backwardation (falling futures price and futures < spot).